NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
Name
7•4
Date
1
1. In New York, state sales tax rates vary by county. In Allegany County, the sales tax rate is 8 2 %.
a.
A book costs $12.99, and a video game costs $39.99. Rounded to the nearest cent, how much more
is the tax on the video game than the tax on the book?
b.
Using 𝑛 to represent the cost of an item in dollars before tax and 𝑡 to represent the amount of sales
tax in dollars for that item, write an equation to show the relationship between 𝑛 and 𝑡.
c.
Using your equation, create a table that includes five possible pairs of solutions to the equation.
Label each column appropriately.
Module 4:
Percent and Proportional Relationships
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NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
7•4
d.
Graph the relationship from parts (b) and (c) in the coordinate plane. Include a title and appropriate
scales and labels for both axes.
e.
Is the relationship proportional? Why or why not? If so, what is the constant of proportionality?
Explain.
Module 4:
Percent and Proportional Relationships
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NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
7•4
f.
In nearby Wyoming County, the sales tax rate is 8%. If you were to create an equation, graph, and
table for this tax rate (similar to parts (b), (c), and (d)), what would the points (0, 0) and (1, 0.08)
represent? Explain their meaning in the context of this situation.
g.
A customer returns an item to a toy store in Wyoming County. The toy store has another location in
Allegany County, and the customer shops at both locations. The customer’s receipt shows $2.12 tax
was charged on a $24.99 item. Was the item purchased at the Wyoming County store or the
Allegany County store? Explain and justify your answer by showing your math work.
Module 4:
Percent and Proportional Relationships
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NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
7•4
1
2. Amy is baking her famous pies to sell at the Town Fall Festival. She uses 32 2 cups of flour for every
10 cups of sugar in order to make a dozen pies. Answer the following questions below and show your
work.
a.
Write an equation, in terms of 𝑓, representing the relationship between the number of cups of flour
used and the number of cups of sugar used to make the pies.
b.
Write the constant of proportionality as a percent. Explain what it means in the context of this
situation.
c.
To help sell more pies at the festival, Amy set the price for one pie at 40% less than what it would
cost at her bakery. At the festival, she posts a sign that reads, “Amy’s Famous Pies—Only
$9.00/Pie!” Using this information, what is the price of one pie at the bakery?
Module 4:
Percent and Proportional Relationships
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NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
7•4
A Progression Toward Mastery
Assessment
Task Item
1
a
7.RP.A.3
7.EE.B.3
b
7.RP.A.2
c
7.RP.A.2
STEP 1
Missing or incorrect
answer and little
evidence of
reasoning or
application of
mathematics to
solve the problem.
STEP 2
Missing or incorrect
answer but
evidence of some
reasoning or
application of
mathematics to
solve the problem.
STEP 3
A correct answer
with some evidence
of reasoning or
application of
mathematics to
solve the problem,
OR an incorrect
answer with
substantial evidence
of solid reasoning or
application of
mathematics to
solve the problem.
STEP 4
A correct answer
supported by
substantial evidence
of solid reasoning or
application of
mathematics to
solve the problem.
Student is not able to
compute the tax for
either item correctly.
Student computes the
tax rate for only one of
the items correctly.
OR
Student computes both
taxes correctly but does
not subtract the two tax
values or does it
incorrectly.
Student computes both
taxes and subtracts the
two tax values correctly
but fails to round the
difference to the nearest
cent.
OR
Student computes both
taxes and subtracts the
two tax values correctly
with only one minor error
in rounding the difference
to the nearest cent.
Student computes both
taxes and subtracts the
two tax values correctly
and correctly rounds the
difference to the nearest
cent.
Student does not
attempt to answer the
question.
Student has the incorrect
answer, writing an
expression such as
0.85𝑛.
Student has the incorrect
answer but makes an
attempt to write an
equation. For example,
the student incorrectly
writes 𝑡 = 0.85𝑛.
Student has the correct
answer: 𝑡 = 0.085𝑛.
Student attempts to
answer the question but
does not construct a
table or only provides
one point.
OR
Student does not
attempt to answer the
question.
Student has the incorrect
answer but makes an
attempt to construct a
table. Fewer than four
correct points are listed.
Student correctly
calculates and lists five
points, but the table is not
labeled correctly.
OR
Student correctly
calculates and lists four of
the five points and
correctly labels the table.
Student has a correct
table (with labeling),
including five points that
show the cost of the item
as the independent
variable and the amount
of sales tax as the
dependent variable.
Student shows significant
evidence of application of
mathematics by
multiplying each cost by
0.085 to get the amount
of sales tax.
Module 4:
Percent and Proportional Relationships
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NYS COMMON CORE MATHEMATICS CURRICULUM
d
7.RP.A.2
7.RP.A.3
e
7.RP.A.2
f
7.RP.A.1
7.RP.A.2
Mid-Module Assessment Task
7•4
Student makes an
attempt to construct a
graph, but the graph is
incomplete, missing
several components.
OR
Student does not
attempt to answer the
question.
Student constructs a
graph that shows some
evidence of
understanding the
proportional
relationship, but the
graph contains multiple
errors. For example, the
scale is incorrect, the
axes are not labeled, the
line is not straight, etc.
Student constructs a
correct graph and uses an
appropriate scale on each
axis but does not label the
axes or provide a title for
the graph.
OR
Student constructs a
correct graph with one
minor error but provides a
title for the graph and
labels the axes correctly.
Student constructs a
correct graph (with
labeling, scale, and title),
showing a straight line
through the origin.
(Scales may vary.)
The cost of the item is
graphed along the 𝑥-axis,
and the amount of sales
tax is graphed along the
𝑦-axis.
Student may or may not
state that the
relationship is
proportional and
provides little or no
evidence of reasoning.
OR
Student does not
attempt to answer the
question.
Student incorrectly
states that the
relationship is not
proportional but
provides an explanation
that demonstrates some
understanding of
proportional
relationships. Student
may or may not identify
a correct constant of
proportionality.
OR
Student correctly
identifies the
relationship as
proportional but states
an incorrect constant of
proportionality.
Student correctly states
that the relationship is
proportional but provides
an incomplete
explanation to support
the claim. For example,
student only includes
“because the graph is a
straight line” and does not
state that it touches the
origin. Student correctly
identifies the constant of
proportionality but may
or may not explain its
meaning.
OR
Student states the
relationship is
proportional but bases
the answer on an
incorrect graph from part
(c). The constant of
proportionality stated is
based on the incorrect
graph.
Student correctly states
that the relationship is
proportional and
provides a thorough
explanation that includes
the following:
(1) the graph is a straight
line that touches the
origin, and (2) all the
ratios of sales tax to cost
equal 0.085. Student
correctly identifies the
constant of
proportionality and
explains its meaning as
the unit rate, identifying
0.085 as the amount of
sales tax per dollar.
Student does not
attempt to answer the
question.
Student incorrectly
explains what (0,0) and
(1, 0.08) mean in the
context of the situation
but provides some
evidence of reasoning.
Student shows solid
evidence of reasoning in
the explanation, but the
answer is not complete.
For example, student
explains that (1, 0.08)
represents the unit rate
and that (0,0) is the point
where there are zero
dollars spent, so no tax is
charged; however,
student does not relate
both points to the context
of the situation.
Student correctly explains
what both points (0, 0)
and (1, 0.08) mean in the
context of the situation.
The explanation includes
evidence of solid
reasoning. For example,
(0, 0) shows nothing was
purchased, so no tax has
been applied, and
(1, 0.08) shows the unit
rate, meaning for every
increase of $1.00, the
amount of tax will
increase by $0.08.
Module 4:
Percent and Proportional Relationships
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This file derived from G7-M4-TE-1.3.0-09.2015
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NYS COMMON CORE MATHEMATICS CURRICULUM
g
7.RP.A.3
7.EE.B.3
2
a
7.RP.A.1
7.RP.A.2
Mid-Module Assessment Task
Student may or may not
answer Allegany County
and provides little or no
evidence of reasoning.
OR
Student does not
attempt to answer the
question.
Student does not have
the correct answer of
Allegany County but
supports the answer with
some evidence of
reasoning. Multiple
errors are made in the
calculations to find the
tax rate.
Student has the correct
answer of Allegany
County, but the math
work or explanation is
slightly incomplete or
contains a minor error.
Student has the correct
answer of Allegany
County and supports the
answer with a valid
explanation and correct
math work (or uses
estimation) to show that
the tax rate is about
8.5%.
Student does not
attempt to answer the
question.
Student writes an
equation involving 𝑓 and
𝑠, but the equation is
incorrect and shows little
evidence of
understanding.
Student writes an
equation involving 𝑓 and
𝑠, and although the
equation is incorrect, it
demonstrates an
understanding of the
proportional relationship.
For instance, the student
writes the equation in
terms of 𝑠, such as
Student writes a correct
equation in terms of 𝑓,
𝑠=
b
7.RP.A.2
c
7.RP.A.3
7.EE.B.3
7•4
1
𝑓.
3.25
1
4
such as 𝑓 = 3 𝑠 or
13
𝑓 = 3.25𝑠 or 𝑓 = 𝑠.
4
Student shows
substantial evidence of
understanding by dividing
32.5 by 10 to find the
constant of
proportionality.
Student answers
incorrectly and shows
little or no evidence of
understanding how to
convert a fraction or
decimal to a percent.
OR
Student does not
attempt to answer the
question.
Student answers
incorrectly, but the math
work and/or explanation
shows some evidence of
understanding how to
convert a fraction or
decimal to a percent.
Student may or may not
have correctly explained
what the constant of
proportionality means in
the context of the
situation.
Student correctly answers
325%, but the
explanation and/or
supporting work is not
complete.
Student correctly
answers 325% with
adequate work shown
AND correctly explains
that the amount of flour
used is 325% of the
amount of sugar used.
Student states an
incorrect price for the pie
and shows little or no
relevant work to support
the answer.
OR
Student does not
attempt to answer the
question.
Student states an
incorrect price for the
pie, but the math work
shows a partial
understanding of the
task involved.
Student states the correct
price of $15 per pie at the
bakery, but the
supporting math work is
incomplete or contains a
minor error.
OR
Student states an
incorrect price for the pie,
but the answer is based
on sound mathematical
work that contains a
minor error.
Student states the
correct price of $15 per
pie at the bakery and
supports the answer with
math work that indicates
solid reasoning and
correct calculations.
For instance, student
may write and solve an
equation such as
9 = (1 − 0.40)𝑥.
Module 4:
Percent and Proportional Relationships
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M4-TE-1.3.0-09.2015
171
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
Name
7•4
Date
1
1. In New York, state sales tax rates vary by county. In Allegany County, the sales tax rate is 8 2 %.
a.
A book costs $12.99 and a video game costs $39.99. Rounded to the nearest cent, how much more
is the tax on the video game than the tax on the book?
b.
Using 𝑛 to represent the cost of an item in dollars before tax and 𝑡 to represent the amount of sales
tax in dollars for that item, write an equation to show the relationship between 𝑛 and 𝑡.
c.
Using your equation, create a table that includes five possible pairs of solutions to the equation.
Label each column appropriately.
Module 4:
Percent and Proportional Relationships
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M4-TE-1.3.0-09.2015
172
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
7•4
d.
Graph the relationship from parts (b) and (c) in the coordinate plane. Include a title and appropriate
scales and labels for both axes.
e.
Is the relationship proportional? Why or why not? If so, what is the constant of proportionality?
Explain.
Module 4:
Percent and Proportional Relationships
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M4-TE-1.3.0-09.2015
173
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
7•4
f.
In nearby Wyoming County, the sales tax rate is 8%. If you were to create an equation, graph, and
table for this tax rate (similar to parts (b), (c), and (d)), what would the points (0, 0) and (1, 0.08)
represent? Explain their meaning in the context of this situation.
g.
A customer returns an item to a toy store in Wyoming County. The toy store has another location in
Allegany County, and the customer shops at both locations. The customer’s receipt shows $2.12 tax
was charged on a $24.99 item. Was the item purchased at the Wyoming County store or the
Allegany County store? Explain and justify your answer by showing your math work.
Module 4:
Percent and Proportional Relationships
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M4-TE-1.3.0-09.2015
174
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM
Mid-Module Assessment Task
7•4
1
2. Amy is baking her famous pies to sell at the Town Fall Festival. She uses 32 2 cups of flour for every
10 cups of sugar in order to make a dozen pies. Answer the following questions below and show your
work.
a. Write an equation, in terms of 𝑓, representing the relationship between the number of cups of flour
used and the number of cups of sugar used to make the pies.
b. Write the constant of proportionality as a percent. Explain what it means in the context of this
situation.
c. To help sell more pies at the festival, Amy set the price for one pie at 40% less than what it would
cost at her bakery. At the festival, she posts a sign that reads, “Amy’s Famous Pies—Only $9.00/Pie!”
Using this information, what is the price of one pie at the bakery?
Module 4:
Percent and Proportional Relationships
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G7-M4-TE-1.3.0-09.2015
175
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.